Availability in Stochastic Models
Published Online: 14 JAN 2011
Copyright © 2010 John Wiley & Sons, Inc. All rights reserved.
Wiley Encyclopedia of Operations Research and Management Science
How to Cite
Mercier, S. 2011. Availability in Stochastic Models. Wiley Encyclopedia of Operations Research and Management Science. .
- Published Online: 14 JAN 2011
A system is considered, which evolves in time according to a stochastic process. The system state space is divided into up- and down-states and the quantities of interest are the system point and asymptotic availabilities, namely the probabilities that the system is in an up-state at some finite time t and as t goes to infinity. Different stochastic continuous-time models and associated tools are presented, such as alternating renewal models, Markov and semi-Markov models, regenerative and Markov regenerative models, with the corresponding renewal or Markov renewal equations fulfilled by the point availability. Classical limit theorems then allow to derive expressions for the asymptotic availability, which involve the process on a generic (Markov) cycle.
- renewal theory;
- Markov renewal theory